Let S=\{z \in C:| z-2| \leq 1, z(1+i)+\overline{z}(1-i) \leq 2\}. Let |z-4 i| attains minimum and maximum values, respectively, at {\z}_1 \in {\S} and {\z}_2 \in {\S}. If 5( z_1|^2+ z_2|^2)=\alpha+\beta \sqrt{5}, where \alpha and \beta are integers, then the value of \alpha+\beta is equal to_____ [29-Jun-2022-Shift-1]

Complex Numbers Part 2

Section: Mathematics

Question : 93 of 97

Marks: +1, -0

Let S={z∈C:|z−2|≤1,z(1+i)+z(1−i)≤2}. Let |z−4i| attains minimum and maximum values, respectively, at z1∈S and z2∈S. If 5(z1|2+z2|2)=α+β√5, where α and β are integers, then the value of α+β is equal to_____

[29-Jun-2022-Shift-1]

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